Problem: Simplify to lowest terms. $\dfrac{8}{12}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 8 and 12? $8 = 2\cdot2\cdot2$ $12 = 2\cdot2\cdot3$ $\mbox{GCD}(8, 12) = 2\cdot2 = 4$ $\dfrac{8}{12} = \dfrac{2 \cdot 4}{ 3\cdot 4}$ $\hphantom{\dfrac{8}{12}} = \dfrac{2}{3} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{8}{12}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{8}{12}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{8}{12}= \dfrac{2\cdot4}{2\cdot6}= \dfrac{2\cdot 2\cdot2}{2\cdot 2\cdot3}= \dfrac{2}{3}$